|Probability, philosophy: If one talks of probability, it is a question of statements applying more or less probable, which describe the course of processes and their results; probability is not about the properties of objects. See also subjective probability, objective probability, probability function, probability distribution, Bayesianism, chance, probability conditional, relative frequency._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
Definition Propensitiy/Popper/Fraassen: Thesis: according to this, probability is itself a physical quantity, the strength or intensity of the real chance of an occurrence or event that cannot be reduced by reference to actual classes of actual occurrences.
Probability/Fraassen: a) epistemic: e.g. 1.75% of the recruits of 44 have survived. - 2. Jones is recruit 44 - 1 and 2 are objective. - But the probability is subjective for me, because I have no further information about Jones. - N.B.: the information that I sum up has not the word "probability" in itself. - Information: that Jones belongs to a certain class. Thus, statistical mechanics has nothing to do with ignorance either.
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Objective Probability/Fraassen. For example, information about the time a system spends in a state is objective information. To call a probability function a measure for something is neither subjective nor objective. - It can also be a measure of ignorance. - objective and subjective (epistemic) probability cannot always be kept apart in practice.
Statistics/probability/infinite/Fraassen: because subregions can be subdivided into even smaller parts ((s) why? - because they end up as points) one needs infinite classes. -> Kolmogoroff axioms (countable additivity). - to map probability onto real numbers. - still extrapolation of finite proportions.
Probability/Quantum mechanics/Fraassen: Problem: Meaningless: half-life of a single atom. - Also for odd numbers of atoms (due to the decay of a half atom). - Solution: subjective probability. I have no further information on this atom. - Problem: objectively accurate ½, subjective: about 1/2 - Problem: there is no relation between exact and approximate! - Solution: in quantum mechanics there is no classic probability.
Mixture/Quantum mechanics: Contrary to pure state: - analog in statistical mechanics: Difference between micro- and macro-state. - Ignorance: to say that the system is in one of e.g. three pure states. - (Ignorance interpretation) - Problem: mixed state: can be decomposed in more than one way.
Probability/Double Slit/Quantum mechanics/Fraassem: must not be equated with the proportions, to find the electron in a certain place.
Infinite/Probability-Theory/Quantum Mechanics/Fraassen: Problem: there are so many pure states and maximal observables as there are real numbers - Probability-Theory: Theorem: if each of a class of mutually exclusive events has a probability > 0, there are only countable many - Problem: then modality comes into play; the probabilities are about what would be the case if ...
Epistemic probability/subjective/Fraassen: can be left to the epistemology. - Objective probability: is a philosophical problem. - What does a probabilistic theory say? - To what are we bound to with this?
Probability Space: 1.K: sample space, event-R, 2.F: family of events, 3.P: Probability measure. - Significance: Problem when too fine-grained. - Definition field: family of subsets of K, completed under the operations average, union, complement formation. - Probability Space: if Field = Borel-Field (Sigma-Field): completed under countable infinitely many unions. - + + Propensity, strict frequency._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
B. van Fraassen
The Scientific Image Oxford 1980